That's what happens when you "drive through." People make the country not, modern buildings and Michelin rated restaurants. If you want everything to look like home, stay there.
Without talking the language, you can't get a grasp on the people, so there is little point in trying. What contact with people I had was better than in Bulagaria and Albania as well, but then Albania was a freaking nightmare of a country, and Bulgaria gives off the vibe that being a crook is how you get ahead in life. (In Albania, that's simply true, there's no uncertainty about it.)
And the run-downness in Romania extends to the people for the most part. But then the only reason to stop anywhere outside the major cities, except for gas, is to get a tire fixed. Plenty of tire shops along national road 1. People drive very dangerously, the number of overtakes into oncoming traffic I've seen was insane.
If you're happy with shitting in a hole, and washing with water heated over a stove, then you can probably make do in rural Romania, but at least from the main road, there's no countryside that you couldn't see elsewhere, besides the actual mountain ranges, which are okay, but in the middle of nowhere, with regard to civilization. Better keep that fuel tank full, because who knows where you can next fill her up.
Stick to the cities, and you get normal Eastern European people that may actually speak a foreign language (if you're lucky, that's English) and have the amenities of civilization. I think I even drank the tap water in Sibiu without consequences. But there's a reason why anybody who has a chance tries to get out of the country and into the EU heartland.
Try the lemonade. Try not to run over/get bitten by any of the dogs. Stay away from agriculture, because it will depress you.
I would recommend a city-hopping trip by plane (Cluj and Bucharest should have airports, not sure about Sibiu. Outside these three, I'm not sure that there's anything else worth seeing, unless you like to walk around run-down 70's soviet-style appartment blocks), and to take a rental car from Bucharest or Sibiu into the mountains. I'm not sure I would recommend hiking, to someone who isn't used to hiking in rough, isolated, terrain, with a variety of wildlife, from wild dogs, to wolves, bears and mosquitoes. If you're a hardcore hiker though, there are a few countryside hotels you can use as staging areas. I've also seen a few bike tourists. I would recommend against that, since driving a bicycle in Romania looked very much like you had 1 in 4 odds of dying in traffic.
There may also be some old castles, but tellingly, along the main roads (and you really don't want to get off those) I have not seen anything that resembles anything from the middle ages.
Of course, OP, you should listen to Magnus' advice and experience how shitty rural Romania really is, but personally, having the sampling I got, I can do without it for the future. It was fun to drive through and see that Eastern Europe still is mostly a shit hole with zero infrastructure, but it wasn't really surprising or amazing. I'm sure if you plan to actually visit Romania, you can find a few interesting spots beforehand, I was constrained by the route I had to take.